Vol. 1, No. 1, 2005

Download this article
Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
Other MSP Journals
On dimensional dual hyperovals ${\mathcal S}^{d+1}_{\sigma,\phi}$

Hiroaki Taniguchi and Satoshi Yoshiara

Vol. 1 (2005), No. 1, 197–219

A d-dimensional dual hyperoval Sσ,ϕd+1 inside PG(2d + 1,2) (d 2) was constructed by Yoshiara, for a generator σ of Gal(GF(q)GF(2)) and an o-polynomial ϕ(X) of GF(q)[X] (q = 2d+1). There, its automorphism group is determined and a criterion is given for these dimensional dual hyperovals to be isomorphic, assuming that the map ϕ on GF(q) induced by ϕ(X) lies in Gal(GF(q)GF(2)). In this paper, we extend these results for a monomial o-polynomial ϕ. We show that Aut(Sσ,ϕd+1)GL3(2) or Zq1.Zd+1 according as d = 2 or d 3, if ϕ(X) is monomial but ϕGal(GF(q)GF(2)). In particular, a special member X(0) of Sσ,ϕd+1 is always fixed by any automorphism of Sσ,ϕd+1. Furthermore, Sσ,ϕd+1Sσ,ϕd+1 if and only if either (σ,ϕ) = (σ,ϕ) or σσ = ϕϕ = id.

dimensional dual hyperoval, o-polynomial
Received: 13 January 2005
Accepted: 17 January 2005
Hiroaki Taniguchi
Satoshi Yoshiara